Travel time: 10.5 hours

The staggered peaks of SkiArena Andermatt-Sedrun (skiarena.ch), which spans three mountains in the Swiss Alps, boast 75 miles of winding, seemingly endless terrain. Expert skiers and snowboarders will be giddy (and woozy) at the top of Gemsstock Mountain—at 9,715 feet, the resort’s tallest—with views of the picturesque Urseren Valley, where the charming medieval village of Andermatt (population 1,543) is seeing a boom in resort development. Across the Oberalp Pass, freestylers play on a 13-foot halfpipe and a tricked-out ski cross and boardercross course. In between mountains, do as the Swiss do and take the edge off with a Schümli Pflümli: hot coffee with plum Schnapps, sugar, and lots of whipped cream.

Lift tickets: From $60

While there: A major crossroads for centuries, Andermatt lies smack in the middle of Zurich and Milan. From February 12 to 17, take a two-hour train ride to lakeside Lucerne for the bizarre, seriously costumed Lucerne Carnival (luzern.com/en/carnival-inlucerne-city), a Mardi Gras celebration that originated in the 15th century. Go for the parades across town and the bands stopping for impromptu sets; steel yourself for the fantastically trippy masks that, fair warning, may freak you out.

Where to stay: The 105-room Chedi Andermatt (from $662, thechedi-andermatt.com), from prolific luxury hotel designer Jean-Michel Gathy, is a behemoth of modern Asian and traditional Alpine design. Arrive to ski butlers who handle your gear—a rarity in the Alps—and big timber-and-stone-clad rooms warmed by fires. The Tibetan-inspired spa is a standout with its Turkish bath, Finnish sauna, 10 suites, and three hydrothermal pools, including one outside.

Getting there: Fly direct to Zurich in eight and a half hours, then take a scenic two-hour train ride to Andermatt.

Lift ticket prices are per day and based on purchase at least a week in advance.